Center-symmetric 1/N expansion

The free energy of U(N) gauge theory is expanded about a center-symmetric topological background configuration with vanishing action and vanishing Polyakov loops. We construct this background for SU(N) lattice gauge theory and show that it uniquely describes center-symmetric minimal action orbits in the limit of infinite lattice volume. The leading contribution to the free energy in the 1/N expansion about this background is of O(N0) rather than O(N2) as one finds when the center symmetry is spontaneously broken. The contribution of planar 't Hooft diagrams to the free energy is O(1/N2) and subleading in this case. The change in behavior of the diagrammatic expansion is traced to Linde's observation that the usual perturbation series of non-Abelian gauge theories suffers from severe infrared divergences [A. Linde, Phys. Lett. B 96, 289 (1980).]. This infrared problem does not arise in a center-symmetric expansion. The 't Hooft coupling λ=g2N is found to decrease ∝1/ln(N) for large N. There is evidence of a vector-ghost in the planar truncation of the model